Extend metamerism index with spectral correction.

colour/colorimetry/__init__.py

@@ -62,6 +62,7 @@
     SD_TO_XYZ_METHODS,
     SPECTRAL_SHAPE_ASTME308,
     adjust_tristimulus_weighting_factors_ASTME308,
+    get_tristimulus_weighting_factors_integration,
     handle_spectral_arguments,
     lagrange_coefficients_ASTME2022,
     msds_to_XYZ,
@@ -223,6 +224,7 @@
     "sd_to_XYZ_ASTME308",
     "sd_to_XYZ_integration",
     "sd_to_XYZ_tristimulus_weighting_factors_ASTME308",
+    "get_tristimulus_weighting_factors_integration",
     "tristimulus_weighting_factors_ASTME2022",
     "wavelength_to_XYZ",
 ]

colour/colorimetry/tristimulus_values.py

@@ -32,6 +32,10 @@
 -   :cite:`ASTMInternational2015b` : ASTM International. (2015). ASTM E308-15 -
     Standard Practice for Computing the Colors of Objects by Using the CIE
     System (pp. 1-47). doi:10.1520/E0308-15
+-   :cite:`InternationalOrganizationforStandardization2024` : International
+    Organization for Standardization. (2024). INTERNATIONAL STANDARD ISO
+    18314-4 - Analytical colorimetry Part 4: Metamerism index for pairs of
+    samples for change of illuminant. https://www.iso.org/standard/85116.html
 -   :cite:`Wyszecki2000bf` : Wyszecki, Günther, & Stiles, W. S. (2000).
     Integration Replaced by Summation. In Color Science: Concepts and Methods,
     Quantitative Data and Formulae (pp. 158-163). Wiley. ISBN:978-0-471-39918-6
@@ -94,6 +98,7 @@
     "lagrange_coefficients_ASTME2022",
     "tristimulus_weighting_factors_ASTME2022",
     "adjust_tristimulus_weighting_factors_ASTME308",
+    "get_tristimulus_weighting_factors_integration",
     "sd_to_XYZ_integration",
     "sd_to_XYZ_tristimulus_weighting_factors_ASTME308",
     "sd_to_XYZ_ASTME308",
@@ -544,6 +549,99 @@ def adjust_tristimulus_weighting_factors_ASTME308(
     return W[start_index : -end_index or None, ...]
 
 
+def get_tristimulus_weighting_factors_integration(
+    cmfs: MultiSpectralDistributions,
+    illuminant: SpectralDistribution,
+    shape: SpectralShape,
+    k: Real | None = None,
+) -> NDArrayFloat:
+    """
+    Return the tristimulus weighting factors computation method for the
+    integration method.
+
+    Parameters
+    ----------
+    cmfs
+        Standard observer colour matching functions.
+    illuminant
+        Illuminant spectral distribution.
+    shape
+        Shape used to build the table, only the interval is needed.
+    k
+        Normalisation constant :math:`k`. For reflecting or transmitting
+        object colours, :math:`k` is chosen so that :math:`Y = 100` for
+        objects for which the spectral reflectance factor
+        :math:`R(\\lambda)` of the object colour or the spectral
+        transmittance factor :math:`\\tau(\\lambda)` of the object is equal
+        to unity for all wavelengths. For self-luminous objects and
+        illuminants, the constants :math:`k` is usually chosen on the
+        grounds of convenience. If, however, in the CIE 1931 standard
+        colorimetric system, the :math:`Y` value is required to be
+        numerically equal to the absolute value of a photometric quantity,
+        the constant, :math:`k`, must be put equal to the numerical value
+        of :math:`K_m`, the maximum spectral luminous efficacy (which is
+        equal to 683 :math:`lm\\cdot W^{-1}`) and
+        :math:`\\Phi_\\lambda(\\lambda)` must be the spectral concentration
+        of the radiometric quantity corresponding to the photometric
+        quantity required.
+
+    Returns
+    -------
+    :class:`numpy.ndarray`
+        Tristimulus weighting factors table.
+
+    References
+    ----------
+    :cite:`InternationalOrganizationforStandardization2024`
+
+    Examples
+    --------
+    >>> from colour import MSDS_CMFS, SDS_ILLUMINANTS
+    >>> cmfs = MSDS_CMFS["CIE 1931 2 Degree Standard Observer"]
+    >>> illuminant = SDS_ILLUMINANTS["D65"]
+    >>> shape = SpectralShape(400, 700, 20)
+    >>> get_tristimulus_weighting_factors_integration(cmfs, illuminant, shape)
+    ... # doctest: +ELLIPSIS
+    array([[  2.23634421e-01,   6.18862548e-03,   1.06034924e+00],
+           [  2.37101690e+00,   7.05764816e-02,   1.13910441e+01],
+           [  6.89706619e+00,   4.55474108e-01,   3.45974172e+01],
+           [  6.46977575e+00,   1.33489183e+00,   3.71366908e+01],
+           [  2.09370011e+00,   3.04335204e+00,   1.77966720e+01],
+           [  1.01189640e-01,   6.67025585e+00,   5.61705756e+00],
+           [  1.25205375e+00,   1.40502317e+01,   1.54849365e+00],
+           [  5.72562903e+00,   1.88094012e+01,   4.00241975e-01],
+           [  1.12268302e+01,   1.87900691e+01,   7.36495171e-02],
+           [  1.65750211e+01,   1.57374968e+01,   2.98469948e-02],
+           [  1.80544399e+01,   1.07252416e+01,   1.35977706e-02],
+           [  1.41509324e+01,   6.30991383e+00,   3.14667619e-03],
+           [  7.07958281e+00,   2.76607946e+00,   3.16123367e-04],
+           [  2.49792489e+00,   9.24035282e-01,   0.00000000e+00],
+           [  6.91427716e-01,   2.51320744e-01,   0.00000000e+00],
+           [  1.53610085e-01,   5.54714053e-02,   0.00000000e+00]])
+    """
+
+    if cmfs.shape != shape:
+        runtime_warning(f'Aligning "{cmfs.name}" cmfs shape to "{shape}".')
+        cmfs = reshape_msds(cmfs, shape, copy=False)
+
+    if illuminant.shape != shape:
+        runtime_warning(f'Aligning "{illuminant.name}" illuminant shape to "{shape}".')
+        illuminant = reshape_sd(illuminant, shape, copy=False)
+
+    XYZ_b = cmfs.values
+    S = illuminant.values
+
+    d_w = cmfs.shape.interval
+
+    # normalisation constant k from Y = 100 of perfect diffuser
+    with sdiv_mode():
+        k = cast("Real", optional(k, sdiv(100, (np.sum(XYZ_b[..., 1] * S) * d_w))))
+
+    # --- weights matrix A (DIN EN ISO 18314-4, eq. 7-8) ---
+    # A[i, :] = k * S(λ_i) * [x̄(λ_i), ȳ(λ_i), z̄(λ_i)] * Δλ
+    return k * S[..., np.newaxis] * XYZ_b * d_w  # shape: (n, 3)
+
+
 def sd_to_XYZ_integration(
     sd: ArrayLike | SpectralDistribution | MultiSpectralDistributions,
     cmfs: MultiSpectralDistributions | None = None,
@@ -724,16 +822,11 @@ def sd_to_XYZ_integration(
         runtime_warning(f'Aligning "{illuminant.name}" illuminant shape to "{shape}".')
         illuminant = reshape_sd(illuminant, shape, copy=False)
 
-    XYZ_b = cmfs.values
-    S = illuminant.values
     R = np.reshape(R, (-1, wl_c_r))
 
-    d_w = cmfs.shape.interval
-
-    with sdiv_mode():
-        k = cast("Real", optional(k, sdiv(100, (np.sum(XYZ_b[..., 1] * S) * d_w))))
+    A = get_tristimulus_weighting_factors_integration(cmfs, illuminant, shape, k)
 
-    XYZ = k * np.dot(R * S, XYZ_b) * d_w
+    XYZ = np.dot(R, A)
 
     XYZ = from_range_100(np.reshape(XYZ, [*list(shape_R[:-1]), 3]))
 

colour/difference/__init__.py

@@ -66,7 +66,11 @@
 )
 from .din99 import delta_E_DIN99
 from .huang2015 import power_function_Huang2015
-from .metamerism_index import Lab_to_metamerism_index, XYZ_to_metamerism_index
+from .metamerism_index import (
+    Lab_to_metamerism_index,
+    XYZ_to_metamerism_index,
+    sd_to_metamerism_index,
+)
 from .stress import INDEX_STRESS_METHODS, index_stress, index_stress_Garcia2007
 
 __all__ = [
@@ -103,6 +107,7 @@
 __all__ += [
     "Lab_to_metamerism_index",
     "XYZ_to_metamerism_index",
+    "sd_to_metamerism_index",
 ]
 
 DELTA_E_METHODS: CanonicalMapping = CanonicalMapping(